Our first computational methods subproject involves using symmetry constraints in molecular modeling and simulations. For those cases in which proteins or protein assemblies are composed of identical subunits, the subunits usually have identical conformations and identical interactions with neighboring subunits. We have incorporated this constraint into our models of ion channels for over two decades, with considerable success. For example our four-fold symmetric model of the ion selective region of potassium channels was virtually identical to those of subsequently determined potassium channel crystal structures. However, until recently, we have not incorporated symmetry constraints into an automated algorithm, nor demonstrated that doing so actually improved the quality of structural models. One of our collaborators, Andriy Anishkin, has developed a program that uses harmonic restraints to restore symmetry during molecular dynamic simulations. We have tested the utility of this program for homology modeling of ion channels by analyzing crystal structures of three distantly related ion channels named KcsA, KirBac, NaK. The first step of this project was to develop two homology models of each channel using the other two channel structures as templates. Next, molecular dynamics simulations of these six models, along with the three crystal structures, were performed with the proteins embedded in an explicit lipid bilayer with water and ions on each side and within the pore of the channels. After eight nanoseconds of unrestrained simulations, symmetry restraints were imposed. This process was repeated two more times for each model and crystal structure. The models developed without molecular dynamic simulations, with unrestrained simulations, and with symmetry-restrained simulations were then compared to the original structures to determine which was better. The major finding was that although unrestrained molecular dynamic simulations did not improve the homology models, imposition of symmetry restraints did lead to substantial improvement. The greatest improvement occurred for the pore lining segments, where interaction among adjacent subunits is extensive. Our principal purpose for developing homology models of ion channels is to understand their structure and pharmacology well enough to utilize the models in structure-based drug design. Thus, it is noteworthy that the symmetry restraints substantially improve models of the pore region that forms the principal drug binding sites. Our second computational methods subproject involves simplifying molecular representations of proteins so that properties of proteins and peptides can be simulated for much longer times. A major limitation of conventional molecular dynamic simulations is that they can be performed for only short periods of time, typically less than a tenth of a microsecond. This is substantially shorter than the time required for most conformational changes, and many orders of magnitude shorter than the time required for assembling amyloid beta structures. To overcome this limit, Dr. Sijung Yun of our group has been using discrete molecular dynamics that is about seven orders of magnitude more efficient than conventional molecular dynamics. He helped develop this program during his doctoral work at the University of Boston. Three simplifications are introduced in discrete molecular dynamics in order to increase efficiency while still preserving accuracy. First, interaction potentials are simplified into discrete steps. This greatly simplifies the mathematics and number of calculations required during the simulations. Second, interactions due to water molecules are replaced by effective potentials. This greatly reduces the number of atoms simulated by eliminating water molecules. Third, we used four-bead representation of a residue in a protein instead of representing all the atoms of the residue. This also reduces the number of simulated atoms. While here, Dr. Yun has worked to improve the parameters and test how well known protein crystal structures are maintained when subjected to these simulations. He has also been using this approach to test models of amyloid-beta hexamers developed by our group. Amyloid-beta hexamers are involved in neurotoxicity of Alzheimers disease. Our third computational methods subproject involves developing models of protein structures on regular lattices. We are using lattices that have the types of symmetry that occur in our models of amyloid beta assemblies. The lattice approach should allow us to examine and evaluate all possible ways of constructing peptide assemblies that have this specific type symmetry. Such exhaustive analysis is not computationally feasible even with simplified discrete molecular dynamics. This project has just been started and we are still evaluating the feasibility of the approach.